We propose to develop new statistical methods for more precise estimation of the influence of one individual on another in a network, testing and controlling for selection effects such as homophily observed between individuals. The work is challenging because network data may contain multiple types of information, including network topology, nodal covariates, tie characteristics, and temporal change. The central problem is accounting for the complex correlation structure that arises because each actor in the network may play the dual role of an ego (rater or responder) and alter (target or stimulus) and thus may appear in the data multiple times. Furthermore, outcomes might be geographically correlated and correlated over time if subjects are followed longitudinally. Here, we focus on development of statistical methodology for longitudinal analysis as this provides the best opportunity for obtaining causal inferences; however, we also propose innovations involving cross-sectional analysis of networks. We have three specific aims: (1) To develop methodology for longitudinal analysis of egocentric data. The objective of such analysis is to determine the causal effect, if any, of an alter adopting a certain health-related behavior or experiencing a certain outcome (e.g., obesity, heart attack) on an ego adopting or experiencing a similar behavior or outcome. Because the correlations between characteristics of egos contain important information on how effects propagate across a population, such models offer the potential to further the scientific understanding of network effects. (2) To develop methods for longitudinal analysis of observations made on distinct groups of connected actors (e.g., dyads, triads). For example, suppose that distinct dyads are defined based on marriage of two individuals; it may be that a property of the tie, such as the quality of the marriage (e.g., measured by strength, mutual affection, time spent together per day), is in turn related to the actors' obesity, the occurrence of health shocks, or the obesity genes in the partners. Although there is a similarity to egocentric analysis, the dependent variable and possibly some of the independent predictors here are measured on groups of connected actors rather than the individual actors. (3) To develop methods for modeling the transition of dyadic data across time as a function of attributes of the actors and of network characteristics (e.g., clustering, transitivity). Here, the dependent variable is defined for all potential dyads whether they exist or not. For most substantive analyses, the dependent variable will be an indicator of whether a tie exists at a given time, in which case we model the transition of the dyad between connected and unconnected states. However, we will also develop methods for the case where the dependent variable is more general (e.g., a count such as the number of patients shared between any two physicians in a network, or some other continuously-valued measure).